Pixelated render output, what am I doing wrong?
From what I see and understand from your description, you are seeing something pretty common when using the Cycles renderer: Noise. (The bright pixels are sometimes referred to as "fireflies")

There are several ways of reducing this effect:
1) Try a higher sample count in the "render" setting 

2) Use one of the denoise options, for example this one: 

3) Switch to Eevee Render Engine: